SQL DB Mail error

I'm trying to send mail via SQL DB Mail.  I have the profile and account setup and working.  When I send email to an internal recipient everything works fine.  But if I try to send to an email address that is not internal, I get this error message:

Cannot send mails to mail server. (Mailbox unavailable. The server response was: 5.7.1 Unable to relay for thoecherl@premiercomputing.com).

The server OS is Server 2003.

How can I fix this?
T HoecherlDeveloperAsked:
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Brett DanneyIT ArchitectCommented:
Your SQL is allowed to send mails internally but the smtp relay on the mail server does not allow external routing. This is a security feature and you would be able to allow the SQL server to be a safe smtp sender.

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Windows Server 2003

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